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Stability of an efficient Navier-Stokes solver with Navier boundary condition
1. | School of Science, East China University of Science and Technology, Shanghai, 200237, China |
2. | Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong |
References:
[1] |
D. Einezl, P. Panzer and M. Liu, Boundary condition for fluid flow: Curved or rough surfaces, Physical Review Letters, 64 (1990), 2269-2272.
doi: 10.1103/PhysRevLett.64.2269. |
[2] |
L. C. Evans, "Partial Differential Equations," 2nd edition, Graduate Studies in Mathematics, 19, Amer. Math. Soc., Providence, RI, 2010. |
[3] |
C. Foias, O. Manley, R. Rosa and R. Temam, "Navier-Stokes Equations and Turbulence," Encyclopedia of Mathematics and its Applications, 83, Cambridge University Press, 2001. |
[4] |
J. L. Guermond, P. Minev and J. Shen, An overview of projection methods for incompressible flows, Comput. Methods Appl. Mech. Engrg., 195 (2006), 6011-6045.
doi: 10.1016/j.cma.2005.10.010. |
[5] |
Q.-L. He and X.-P. Wang, Numerical study of the effect of Navier slip on the driven cavity flow, Z. Angew. Math. Mech., 89 (2009), 857-868.
doi: 10.1002/zamm.200900245. |
[6] |
O. A. Ladyzhenskaya, "The Mathematical Theory of Viscous Incompressible Flow," 2nd English edition, revised and enlarged, Mathematics and its Applications, Vol. 2, Gordon and Breach, Science Publishers, New York-London-Paris, 1969. |
[7] |
J.-G. Liu, J. Liu and R. L. Pego, Divorcing pressure from viscosity in incompressible Navier-Stokes dynamics,, preprint, ().
|
[8] |
J.-G. Liu, Jie Liu and R. Pego, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate, Comm. Pure Appl. Math., 60 (2007), 1443-1487.
doi: 10.1002/cpa.20178. |
[9] |
C. L. M. H. Navier, Memoire sur les lois du mouvement des fluides, Mem. Acad. R. Sci. Inst. Fr., 6 (1823), 389-440. |
[10] |
C. Neto, D. R. Evans, E. Bonaccurso, H.-J. Butt and V. S. J. Craig, Boundary slip in Newtonian liquids: A review of experimental studies, Rep. Prog. Phys., 68 (2005), 2859-2897.
doi: 10.1088/0034-4885/68/12/R05. |
[11] |
T.-Z. Qian and X.-P. Wang, Driven cavity flow: From molecular dynamics to continuum hydrodynamics, Multiscale Model. Simul., 3 (2005), 749-763.
doi: 10.1137/040604868. |
show all references
References:
[1] |
D. Einezl, P. Panzer and M. Liu, Boundary condition for fluid flow: Curved or rough surfaces, Physical Review Letters, 64 (1990), 2269-2272.
doi: 10.1103/PhysRevLett.64.2269. |
[2] |
L. C. Evans, "Partial Differential Equations," 2nd edition, Graduate Studies in Mathematics, 19, Amer. Math. Soc., Providence, RI, 2010. |
[3] |
C. Foias, O. Manley, R. Rosa and R. Temam, "Navier-Stokes Equations and Turbulence," Encyclopedia of Mathematics and its Applications, 83, Cambridge University Press, 2001. |
[4] |
J. L. Guermond, P. Minev and J. Shen, An overview of projection methods for incompressible flows, Comput. Methods Appl. Mech. Engrg., 195 (2006), 6011-6045.
doi: 10.1016/j.cma.2005.10.010. |
[5] |
Q.-L. He and X.-P. Wang, Numerical study of the effect of Navier slip on the driven cavity flow, Z. Angew. Math. Mech., 89 (2009), 857-868.
doi: 10.1002/zamm.200900245. |
[6] |
O. A. Ladyzhenskaya, "The Mathematical Theory of Viscous Incompressible Flow," 2nd English edition, revised and enlarged, Mathematics and its Applications, Vol. 2, Gordon and Breach, Science Publishers, New York-London-Paris, 1969. |
[7] |
J.-G. Liu, J. Liu and R. L. Pego, Divorcing pressure from viscosity in incompressible Navier-Stokes dynamics,, preprint, ().
|
[8] |
J.-G. Liu, Jie Liu and R. Pego, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate, Comm. Pure Appl. Math., 60 (2007), 1443-1487.
doi: 10.1002/cpa.20178. |
[9] |
C. L. M. H. Navier, Memoire sur les lois du mouvement des fluides, Mem. Acad. R. Sci. Inst. Fr., 6 (1823), 389-440. |
[10] |
C. Neto, D. R. Evans, E. Bonaccurso, H.-J. Butt and V. S. J. Craig, Boundary slip in Newtonian liquids: A review of experimental studies, Rep. Prog. Phys., 68 (2005), 2859-2897.
doi: 10.1088/0034-4885/68/12/R05. |
[11] |
T.-Z. Qian and X.-P. Wang, Driven cavity flow: From molecular dynamics to continuum hydrodynamics, Multiscale Model. Simul., 3 (2005), 749-763.
doi: 10.1137/040604868. |
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